With the setting ExtentSize->{sl,sr}, a horizontal line is drawn around each plot point, extending sl to the left and sr to the right. With ExtentMarkers->{ml,mr}, the markers ml and mr will be used as left and right extent boundary markers.

With the default settings Joined->Automatic and Filling->Axis, DiscretePlot switches between drawing points with a stem filling when there are few points and lines with a solid filling when there are many points.

The arguments supplied to ExtentElementFunction are the element region {{xmin,xmax},{ymin,ymax}} and the sample point {xi,yi}.